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Machine learning potentials (MLPs) offer efficient and accurate material simulations, but constructing the reference ab initio database remains a significant challenge, particularly for catalyst-adsorbate systems. Training an MLP with a small dataset can lead to overfitting, thus limiting its practical applications. This study explores the feasibility of developing computationally cost-effective and accurate MLPs for catalyst-adsorbate systems with a limited number of ab initio references by leveraging a transfer learning strategy from subsets of a comprehensive public database. Using the Open Catalyst Project 2020 (OC20) -- a dataset closely related to our system of interest -- we pre-trained MLP models on OC20 subsets using the {\ae}net-PyTorch framework. We compared several strategies for database subset selection. Our findings indicate that MLPs constructed via transfer learning exhibit better generalizability than those constructed from scratch, as demonstrated by the consistency in the dynamics simulations. Remarkably, transfer learning enhances the stability and accuracy of MLPs for the CuAu/H2O system with approximately 600 reference data points. This approach achieved excellent extrapolation performance in molecular dynamics (MD) simulations for the larger CuAu/6H2O system, sustaining up to 250 ps, whereas MLPs without transfer learning lasted less than 50 ps. We also examine the potential limitations of this strategy. This work proposes an alternative, cost-effective approach for constructing MLPs for the challenging simulation of catalytic systems. Finally, we anticipate that this methodology will pave the way for broader applications in material science and catalysis research, facilitating more efficient and accurate simulations across various systems., Comment: 41 pages, 11 figures, 10 SI figures

There is a growing demand for simulators for the research and development of maritime autonomous surface ships (MASS) and the approval of autonomous navigation algorithms. Simulators are used for purposes such as evaluation and training and are taken on various configurations accordingly. The ship maneuvering mathematical model used in such a simulator is an important element that characterizes the simulator. In this paper, we discuss the dynamic model of the hull and its position in the simulator that will be required for MASSs in the future. It also discusses guidelines for selecting an appropriate model, which has not been discussed extensively in previous studies. Finally, we discuss the functional requirements that simulators should have., Comment: 21 pages, 3 figures, Submitted to Journal of Marine Science and Technology

Ponzi schemes, defined by Block-Weinberger(1992) and Roe(2003), give a characterization of amenability from the viewpoint of coarse geometry. We consider measures in coarse spaces, and propose a reformulation of Ponzi schemes with measures., Comment: 20pages.Comments are welcome

In this paper, we establish Multilayer Correlation Clustering, a novel generalization of Correlation Clustering (Bansal et al., FOCS '02) to the multilayer setting. In this model, we are given a series of inputs of Correlation Clustering (called layers) over the common set $V$. The goal is then to find a clustering of $V$ that minimizes the $\ell_p$-norm ($p\geq 1$) of the disagreements vector, which is defined as the vector (with dimension equal to the number of layers), each element of which represents the disagreements of the clustering on the corresponding layer. For this generalization, we first design an $O(L\log n)$-approximation algorithm, where $L$ is the number of layers, based on the well-known region growing technique. We then study an important special case of our problem, namely the problem with the probability constraint. For this case, we first give an $(\alpha+2)$-approximation algorithm, where $\alpha$ is any possible approximation ratio for the single-layer counterpart. For instance, we can take $\alpha=2.5$ in general (Ailon et al., JACM '08) and $\alpha=1.73+\epsilon$ for the unweighted case (Cohen-Addad et al., FOCS '23). Furthermore, we design a $4$-approximation algorithm, which improves the above approximation ratio of $\alpha+2=4.5$ for the general probability-constraint case. Computational experiments using real-world datasets demonstrate the effectiveness of our proposed algorithms.

We study the classic problem of prediction with expert advice under bandit feedback. Our model assumes that one action, corresponding to the learner's abstention from play, has no reward or loss on every trial. We propose the CBA algorithm, which exploits this assumption to obtain reward bounds that can significantly improve those of the classical Exp4 algorithm. We can view our problem as the aggregation of confidence-rated predictors when the learner has the option of abstention from play. Importantly, we are the first to achieve bounds on the expected cumulative reward for general confidence-rated predictors. In the special case of specialists we achieve a novel reward bound, significantly improving previous bounds of SpecialistExp (treating abstention as another action). As an example application, we discuss learning unions of balls in a finite metric space. In this contextual setting, we devise an efficient implementation of CBA, reducing the runtime from quadratic to almost linear in the number of contexts. Preliminary experiments show that CBA improves over existing bandit algorithms.

Centrality measures, quantifying the importance of vertices or edges, play a fundamental role in network analysis. To date, triggered by some positive approximability results, a large body of work has been devoted to studying centrality maximization, where the goal is to maximize the centrality score of a target vertex by manipulating the structure of a given network. On the other hand, due to the lack of such results, only very little attention has been paid to centrality minimization, despite its practical usefulness. In this study, we introduce a novel optimization model for local centrality minimization, where the manipulation is allowed only around the target vertex. We prove the NP-hardness of our model and that the most intuitive greedy algorithm has a quite limited performance in terms of approximation ratio. Then we design two effective approximation algorithms: The first algorithm is a highly-scalable algorithm that has an approximation ratio unachievable by the greedy algorithm, while the second algorithm is a bicriteria approximation algorithm that solves a continuous relaxation based on the Lov\'asz extension, using a projected subgradient method. To the best of our knowledge, ours are the first polynomial-time algorithms with provable approximation guarantees for centrality minimization. Experiments using a variety of real-world networks demonstrate the effectiveness of our proposed algorithms: Our first algorithm is applicable to million-scale graphs and obtains much better solutions than those of scalable baselines, while our second algorithm is rather strong against adversarial instances., Comment: Accepted to The Web Conference 2024

We study a general clustering setting in which we have $n$ elements to be clustered, and we aim to perform as few queries as possible to an oracle that returns a noisy sample of the similarity between two elements. Our setting encompasses many application domains in which the similarity function is costly to compute and inherently noisy. We propose two novel formulations of online learning problems rooted in the paradigm of Pure Exploration in Combinatorial Multi-Armed Bandits (PE-CMAB): fixed confidence and fixed budget settings. For both settings, we design algorithms that combine a sampling strategy with a classic approximation algorithm for correlation clustering and study their theoretical guarantees. Our results are the first examples of polynomial-time algorithms that work for the case of PE-CMAB in which the underlying offline optimization problem is NP-hard.

In this paper, we give the Jacobi identity of Toda brackets indexed by $n$, ($n \geq 0$), this generalizes Toda's Jacobi identity of Toda brackets indexed by 0 shown in [T].

In this paper, we give an unstable approach of the May-Lawrence matrix Toda bracket, which becomes a useful tool for the theory of determinations of unstable homotopy groups. Then, we give a generalization of the classical isomorphisms between homotopy groups of $(JS^{m},S^{m}) $ and $(JS^{2m},*)$ localized at 2. After that we provide a generalized $H$-formula for matrix Toda brackets. As an application, we show a new construction of $\ct'\in\pi_{26}(S^{6})$ localized at 2 which improves the construction of $\ct'$ given by \cite{20STEM}.

We extend the former results of Ganea and the two of the authors with Takeda on the homotopy commutativity of the loop spaces of Hermitian symmetric spaces such that the loop spaces of all irreducible symmetric spaces but $\mathbb{C}P^3$ are not homotopy commutative., Comment: 11pages

Dense subgraph discovery methods are routinely used in a variety of applications including the identification of a team of skilled individuals for collaboration from a social network. However, when the network's node set is associated with a sensitive attribute such as race, gender, religion, or political opinion, the lack of diversity can lead to lawsuits. In this work, we focus on the problem of finding a densest diverse subgraph in a graph whose nodes have different attribute values/types that we refer to as colors. We propose two novel formulations motivated by different realistic scenarios. Our first formulation, called the densest diverse subgraph problem (DDSP), guarantees that no color represents more than some fraction of the nodes in the output subgraph, which generalizes the state-of-the-art due to Anagnostopoulos et al. (CIKM 2020). By varying the fraction we can range the diversity constraint and interpolate from a diverse dense subgraph where all colors have to be equally represented to an unconstrained dense subgraph. We design a scalable $\Omega(1/\sqrt{n})$-approximation algorithm, where $n$ is the number of nodes. Our second formulation is motivated by the setting where any specified color should not be overlooked. We propose the densest at-least-$\vec{k}$-subgraph problem (Dal$\vec{k}$S), a novel generalization of the classic Dal$k$S, where instead of a single value $k$, we have a vector ${\mathbf k}$ of cardinality demands with one coordinate per color class. We design a $1/3$-approximation algorithm using linear programming together with an acceleration technique. Computational experiments using synthetic and real-world datasets demonstrate that our proposed algorithms are effective in extracting dense diverse clusters., Comment: Accepted to KDD 2023

A dynamic model for an automatic berthing and unberthing controller has to estimate harbor maneuvers, which include berthing, unberthing, approach maneuvers to berths, and entering and leaving the port. When the dynamic model is estimated by the system identification, a large number of tests or trials are required to measure the various motions of harbor maneuvers. However, the amount of data that can be obtained is limited due to the high costs and time-consuming nature of full-scale ship trials. In this paper, we improve the generalization performance of the dynamic model for the automatic berthing and unberthing controller by introducing data augmentation. This study used slicing and jittering as data augmentation methods and confirmed their effectiveness by numerical experiments using the free-running model tests. The dynamic model is represented by a neural network-based model in numerical experiments. Results of numerical experiments demonstrated that slicing and jittering are effective data augmentation methods but could not improve generalization performance for extrapolation states of the original dataset., Comment: 12 pages, 11 figures, Submitted to Journal of Marine Science and Technology